US8194527B2 - Interleaving with iterative calculation of interleaving addresses - Google Patents
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
- H03M13/276—Interleaving address generation
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
Abstract
Description
I(k)−k=Q(k)×p (1)
in which k={0, . . . , K−1} and Q(k) is a function in the relative integer space such that, whatever the value of k: Q(k)×p<K.
I(k)=[s+kd] K where k={0, . . . , K−1}, d=|I(k+1)−I(k)|
where E(z) is the integer part of z.
K=n×(d−1)=n×m×p (2)
-
- a first step of calculating an intermediate value I0 (j)(k) that for the first iteration (j=1) is the result of applying a first algebraic function f0(a, b) modulo K with two variables a and b to the input indices k, a=b=k and for each subsequent iteration j(j=2 to N) is the result of applying the same algebraic function f0(a, b) to the input indices k and to an output value I(j−1)(k) obtained during the preceding iteration;
- a second step of calculating the output value I(j)(k) that, for a given iteration j, is the result of applying a second algebraic function f1(a, b) modulo K with two variables a and b to the input indices k and to the intermediate value I0 (j)(k) calculated in the same iteration j, a=k and b=I0 (j)(k). The first algebraic function f0(a, b) and the second algebraic function f1(a, b) are linked so that, on each iteration j, the difference between the position index of the interleaved data item and its rank in the interleaved sequence is the product modulo K of a parameter p depending on the size of a pattern to be preserved and the sum of a natural integer parameter a that can vary from 0 to K/p and a multiple of the intermediate value.
-
- K, the block size to be interleaved;
- p, which depends on the size of a pattern to be preserved;
- q, which adds a degree of freedom to the adjustment of the interleaving law;
- N, the number of iterations.
Pj,s(k)=I (j)(k+s)−I (j)(k) (3)
where s<K
-
- the interleaving spreading ΔeffI(j)(s) between two successive data items of the overall data stream, s=1;
- the interleaving spreading ΔeffI(j)(s) of data items from the same stream i, i={1, . . . , p}, s=p;
- the interleaving spreading ΔeffI(j)(s) between two data items separated by L−1 data items where L is fixed by an external constraint, s=L; that constraint can be:
- the distribution of the bits at the time of binary to symbol coding;
- specific formatting of the data for transmission.
-
- ensures a maximum distance between the position indices associated with data items of the same weight in symbols after binary to symbol coding followed by digital modulation;
- specifically orders the data for transmission of the data on the physical medium.
f 0(a,b)=[−a−pb] K (4)
and the second algebraic function f1(a,b) has the expression:
f 1(a,b)=[αp+a+qpb] K (5)
I 0 (1)(k)=f 0(k,k)=[−k−pk] K (6)
and after each subsequent iteration in the form:
I 0 (j)(k)=f 0(k,I (j−1)(k))=[−k−p·I (j−1)(k)]K (7)
I (j)(k)=I 1 (j)(k)=f 1(k,I 0 (j)(k))=[αp+k+q·p·I 0 (j)(k)]K (8)
where q and α are parameters that are typically natural integers, α varying from 0 to K/p.
Y(k)=X(I(k)) where k={0, . . . , K−1} and I(k)={0, . . . , K−1}.
I 0 (j)(k)=[−a−bp] K.
I 0 (1)(k)=[−k−kp] K where k={0, . . . , K−1} (9)
I 0 (j)(k)=[−k−I (j−1)(k)×p] K (10)
I (j)(k)=f 1(k,I 0 (j)(k)) (11)
f 1(a,b)=[αp+a+q·p·b] K
which yields, for I(j)(k):
I (j)(k)=f 1(a,b)=[αp+k+q·p·I 0 (j)(k)]K (12)
in which α is a natural integer varying from 0 to K/p and q is a parameter that is a natural integer.
I (j)(k)=[K−p+k+q·p·I 0 (j)(k)]K
I 0(k)=f 0(k,b)=[−k−bp] K where k={0, . . . , K−1} (13)
and:
I 1(k)=f 1(k,b)=[αp+k+b·p·q] K where k={0, . . . , K−1}(14)
I 0 (1)(k)=f 0(k,k)=[−k−kp] K where k={0, . . . , K−1} (15)
I 1(k)=f 1(k,I 0(k))=[αp+k+I 0(k)·p·q] K where k={0, . . . , K−1} (16)
I(k)=f(p,q,k,K)=[αp+k+I 0(k)·p·q] K where k={0, . . . , K−1} (17)
I (1)(k)=[αp+k+p·q·[−k−k·p] K]K where k={0, . . . , K−1} (18)
I 0 (2)(k)=[−k−p×I (1)(k)]K where k={0, . . . , K−1}
and the interleaving law is given by:
I (2)(k)=[αp+k+I 0 (2)(k)·p·q] K where k={0, . . . , K−1}
I (2)(k)=[αp+k+p·q·[−k−p·I (1)(k)]K]K
and more generally, for iteration j:
I 0 (j)(k)=[−k−p·I (j−1)(k)]K k={0, . . . , K−1} (19)
and the interleaving law for iteration j is given by:
I (j)(k)=[αp+k+p·q·I 0 (j)(k)]K k={0, . . . , K−1}
I (j)(k)=[αp+k+p·q·[−k−p·I (j−1)(k)]K]K k={0, . . . , K−1} (20)
I (j)(k)−k=Q(k)×p where k={0, . . . , K−1};
where Q(k) is a function in the relative integers space Z such that, for any value of k, Q(k)×p<K.
I (j)(k)−k=[αp+p·q·I 0 (j)(k)]K k={0, . . .K−1}
I (j)(k)−k=p[α+q·[−k−p·I (j−1)(k)]K]K k={0, . . .K−1} (21)
[a+b] N =[[a] N +[b] N]N
[a·b] N =[[a] N ·[b] N]N
ΔI (1)(k)=I (1)(k+1)−I (1)(k)
ΔI c (1)(k)=K−|Δ (1) I(k)| and
the interleaving spreading is given by the equation:
Δeff I (1)(s=1)=Min {|I (1)(k+1)−I (1)(k)|, K−|I (1)(k+1)−I (1)(k)|}
Δeff I (1)(s=1)=Min {|ΔI (1)(k)|, K−|ΔI (1)(k)|}=Min {|[1−q·p(1+p)]K |, K−|[1−q·p(1+p)]K|}
because:
I (1)(k)=[αp+k+qp[−k−pk] K]K k={0, . . . , K−1}
I (1)(k+1)=[αp+k+1+qp[−(k+1)−p(k+1)]K]K
ΔI (1)(k)=[1−qp(p+1)]K
Δeff I (2)(s=1)=Min {|ΔI (2)(k)|, K−|ΔI (2)(k)|}=Min {|[1−qp(1+pΔI (1)(k))]K |, K−|[1−qp(1+pΔI (1)(k))]K|}
because:
I (2)(k)=[αp+k+qpI 0 (2)(k)]K =[αp+k−qp[k+pI (1)(k)]K]K
ΔI (2)(k)=I (2)(k+1)=I (2)(k)=[1−qp(1+pΔI (1)(k))]K
where k={0, . . . , K−1} and
Δeff I (j)(s=1)=Min {|ΔI (j)(k)|, K−|ΔI (j)(k)|}=Min {|[1−qp(1+pΔI (j−1)(k))]K |, K−|[1−qp(1+pΔI (j−1)(k))]K|}
because:
I (j)(k)=[αp+k+qpI 0 (j)(k)]K =[αp+k+qp[−k−pI (j−1) (k)]K]K k={0, . . . , K−1}
ΔI (j)(k)=[1−qp(1+pΔI (j−1)(k))]K
The size of the observation window during which the difference ΔI(j)(k) is constant is expressed in the following form, to the nearest data item: for
where E{Z} is the integer part of Z, and:
for iteration j.
Δeff I (j)(s)=Min {|[s−q·p(s+pP j,s(k))]K |, K−|[s−qp(s+pP j,s(k))]K|}
where:
P j,s(k)=I (j)(k+s)−I (j)(k)=[s−q·p·(s+p·P j−1,s(k))]K
P 1,s(k)=[s−qp×s(p+1)]K
-
- Step 1) selecting p and q for an interleaving size K, where K is a multiple of p.
- Step 2) estimating the interleaving spreading ΔeffI(j)(s=1) and the maximum interleaving spreading over a pseudoperiod: ΔeffI(j)(s=L(j)(p,q)−1)=(L(j)(p,q)−1)·ΔeffI(j)(s=1).
- Step 3) for one or more external constraints, evaluating the interleaving spreading ΔeffI(j)(s) for different values of j between data items separated by s−1 data items in relation to the external constraint that fixes the value of the integer parameter s.
- Step 4) selecting the iteration j that yields the greatest interleaving spreading between data items separated by s−1 data items in circumstances where s is fixed by an external constraint and s=L(j)(p,q)−1. If there is more than one iteration producing identical values with a different interleaving law, the iteration that yields the greatest interleaving spreading between successive data items is selected.
- repeating steps 1), 2), 3) if the values of p and q are not the optimum in relation to one or more thresholds So(s) set by the user. If p is imposed by an external constraint, then only the value q is modified.
TABLE 1 |
interleaving law for the RP technique with |
K = 60 and p = 23, calculation of R′. |
k | I (k) | R′ (k) |
0 | 0 | 0 |
1 | 23 | 7.33 |
2 | 46 | 14.7 |
3 | 9 | 2 |
4 | 32 | 9.33 |
5 | 55 | 16.7 |
6 | 18 | 4 |
7 | 41 | 11.3 |
8 | 4 | −1.33 |
9 | 27 | 6 |
10 | 50 | 13.3 |
11 | 13 | 0.67 |
12 | 36 | 8 |
13 | 59 | 15.3 |
14 | 22 | 2.67 |
15 | 45 | 10 |
16 | 8 | −2.67 |
17 | 31 | 4.67 |
18 | 54 | 12 |
19 | 17 | −0.67 |
20 | 40 | 6.67 |
21 | 3 | −6 |
22 | 26 | 1.33 |
23 | 49 | 8.67 |
24 | 12 | −4 |
25 | 35 | 3.33 |
26 | 58 | 10.7 |
27 | 21 | −2 |
28 | 44 | 5.33 |
29 | 7 | −7.33 |
30 | 30 | 0 |
31 | 53 | 7.33 |
32 | 16 | −5.33 |
33 | 39 | 2 |
34 | 2 | −10.7 |
35 | 25 | −3.33 |
36 | 48 | 4 |
37 | 11 | −8.67 |
38 | 34 | −1.33 |
39 | 57 | 6 |
40 | 20 | −6.67 |
41 | 43 | 0.67 |
42 | 6 | −12 |
43 | 29 | −4.67 |
44 | 52 | 2.67 |
45 | 15 | −10 |
46 | 38 | −2.67 |
47 | 1 | −15.3 |
48 | 24 | −8 |
49 | 47 | −0.67 |
50 | 10 | −13.3 |
51 | 33 | −6 |
52 | 56 | 1.33 |
53 | 19 | −11.3 |
54 | 42 | −4 |
55 | 5 | −16.7 |
56 | 28 | −9.33 |
57 | 51 | −2 |
58 | 14 | −14.7 |
59 | 37 | −7.33 |
TABLE 2 |
Interleaving spreading of interleaved data |
64-QAM | 16-QAM | ||||
ΔeffI(j) (s = 1) | L(j) (k) | ΔeffI(j) (k, s = 6) | ΔeffI(j) (k, s = 4) | ||
|
23 | 3 | 18 | 28 |
|
11 | 5 | 6 | 16 |
|
13 | 5 | 18 | 18 |
TABLE 3 |
Interleaving spreading for different values |
of p, q = 2 and 64-QAM modulation |
ΔeffI(j) (s = 1) | L (s = 1) | ΔeffI(j) (k, s = 6) |
It. | It. | It. | |||||||||
K | p | K/p | It. 1 | It. 2 | 3 | It. 1 | It. 2 | 3 | It. 1 | It. 2 | 3 |
60 | 3 | 20 | 23 | 11 | 13 | 3 | 5 | 5 | 18 | 6 | 18 |
60 | 6 | 10 | 23 | 25 | 11 | 3 | 2 | 5 | 18 | 30 | 6 |
60 | 12 | 5 | 11 | 25 | 23 | 5 | 2 | 3 | 6 | 30 | 18 |
60 | 15 | 4 | 1 | 1 | 1 | 60 | 60 | 60 | 6 | 6 | 6 |
60 | 20 | 3 | 1 | 1 | 1 | 60 | 60 | 60 | 6 | 6 | 6 |
TABLE 4 |
Interleaving spreading for different values |
of p, q = 2 and 16-QAM modulation |
ΔeffI(j) (s = 1) | L (s = 1) | ΔeffI(j) (k, s = 4) |
It. | It. | It. | |||||||||
K | p | K/p | It. 1 | It. 2 | 3 | It. 1 | It. 2 | 3 | It. 1 | It. 2 | 3 |
60 | 3 | 20 | 23 | 11 | 13 | 3 | 5 | 5 | 28 | 16 | 8 |
60 | 6 | 10 | 23 | 25 | 11 | 3 | 2 | 5 | 28 | 20 | 16 |
60 | 12 | 5 | 11 | 25 | 23 | 5 | 2 | 3 | 16 | 20 | 28 |
60 | 15 | 4 | 1 | 1 | 1 | 60 | 60 | 60 | 4 | 4 | 4 |
60 | 20 | 3 | 1 | 1 | 1 | 60 | 60 | 60 | 4 | 4 | 4 |
60 | 30 | 2 | 1 | 1 | 1 | 60 | 60 | 60 | 4 | 4 | 4 |
TABLE 5 |
OFDM parameters associated with the transmission system |
OFDM parameters and coding | Value |
Npm: Number of sub-carriers | 177 |
ΔF: sub-carrier spacing | 19.5 | kHz |
NFFT: IFFT/FFT | 256 |
TCP: cyclic prefix duration/guard | 4.2 | μs |
TFFT: useful OFDM symbol time | 51.2 | μs |
duration/FFT period | ||
TSYM: OFDM symbol total duration | 55.4 | μs (TCP + TFFT) |
Fe: |
5 | MHz |
FOCTC coding, code rate r = 1/3 | RSC elementary code |
generator polynomials | |
(25 bytes, 37 bytes) | |
FOCTC internal interleaving matrix | Invention with p = 20, q = 2, |
parameters | Kint = 1440, |
TABLE 6 |
Interleaving pattern parameters |
No. of | ||||||
ΔIeff (s = | branches | ΔIeff (s = | ||||
p | ΔIeff (s = 1) | L) | L | 6) | ||
|
6 × 1440 = | 17279 | 6 | 6 | 6 |
8640 | |||||
|
240 | 11999 | 4311 | 9 | 71294 |
|
1440 | 2879 | 36 | 36 | 17274 |
|
36 | 2663 | 177 | 39 | 15978 |
RP | 17279 | 173279 | |||
Claims (19)
I (1)(k)=[αp+k+p·q·[−k−k·p] K]K; and
I (j)(k)=[αp+k+p·q·[−k−p·I (j-i)(k)]K]K
I (1)(k)=[αp+k+p·q·[−k−k·p] K]K; and
I (j)(k)=[αp+k+p·q·[−k−p·I (j-1)(k)]K]K
I (1)(k)=[αp+k+p·q·[−k−k·p] K]K; and
I (j)(k)=[αp+k+p·q·[−k−p·I (j-1)(k)]K]K
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FR0414113 | 2004-12-31 | ||
FR0414113A FR2880483A1 (en) | 2004-12-31 | 2004-12-31 | INTERLACING METHOD AND DEVICE |
PCT/FR2005/003237 WO2006072694A1 (en) | 2004-12-31 | 2005-12-19 | Interleaving with iterative calculation of interleaving addresses |
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CN (1) | CN101133559B (en) |
AT (1) | ATE425587T1 (en) |
DE (1) | DE602005013305D1 (en) |
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JP2008527768A (en) | 2008-07-24 |
EP1864383A1 (en) | 2007-12-12 |
WO2006072694A1 (en) | 2006-07-13 |
PL1864383T3 (en) | 2009-07-31 |
EP1864383B1 (en) | 2009-03-11 |
ATE425587T1 (en) | 2009-03-15 |
CN101133559B (en) | 2011-05-04 |
EP1986330A1 (en) | 2008-10-29 |
KR101227560B1 (en) | 2013-01-29 |
CN101133559A (en) | 2008-02-27 |
EP1986330B1 (en) | 2019-08-07 |
ES2323185T3 (en) | 2009-07-08 |
JP5129576B2 (en) | 2013-01-30 |
DE602005013305D1 (en) | 2009-04-23 |
KR20070104378A (en) | 2007-10-25 |
US20100008214A1 (en) | 2010-01-14 |
FR2880483A1 (en) | 2006-07-07 |
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